Khot's Unique Games Conjecture in transversal-polynomial form

Let $X^{\alpha}$ be an $r$-fold cover of a graph $X$, where $\xi(X^{\alpha},t)$ is the transversal polynomial and $\deg(\xi(X^{\alpha},t))$ is the maximum number of edges satisfied by a labelling of $X$. For all $\epsilon,\delta>0$, there exists $r=r(\epsilon,\delta)$ such that, given an $r$-fold cover $X^{\alpha}$ of a graph $X$, it is NP-hard to distinguish between the following two cases:

1. $\deg(\xi(X^{\alpha},t))\geq(1-\epsilon)|E(X)|$;
2. $\deg(\xi(X^{\alpha},t))\leq\delta|E(X)|$.

This is the Unique Games Conjecture, a central complexity-theoretic hypothesis whose truth would imply optimality results for approximation algorithms for several NP-hard problems. In this formulation, the degree of the transversal polynomial records the maximum number of edges satisfied by a labelling; the source provides no resolution of the conjecture.